Question: Simplify the following expression: $p = \dfrac{8n^2 - 12n}{-8n}$ You can assume $n \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $8n^2 - 12n = (2\cdot2\cdot2 \cdot n \cdot n) - (2\cdot2\cdot3 \cdot n)$ The denominator can be factored: $-8n = - (2\cdot2\cdot2 \cdot n)$ The greatest common factor of all the terms is $4n$ Factoring out $4n$ gives us: $p = \dfrac{(4n)(2n - 3)}{(4n)(-2)}$ Dividing both the numerator and denominator by $4n$ gives: $p = \dfrac{2n - 3}{-2}$